The South China Sea is the most important body of water for the world economy—through it passes at least one-third of global trade. It is also the most dangerous body of water in the world, the place where the militaries of the United States and China could most easily collide.

Chinese and American warships have just barely averted several incidents there over the past few years, and the Chinese military has warned off U.S. jets flying above. In July, the two nations carried out competing naval exercises in those waters. Given what is called the growing “strategic rivalry” between Washington and Beijing, the specter of an accident that in turn triggers a larger military confrontation preoccupies strategists in both capitals.

These tensions grow out of a disagreement between the two countries as to whether the South China Sea is Chinese territory, a quarrel that speaks to a deeper dispute about maritime sovereignty, how it is decided upon, and the fundamental rights of movement in those waters.

The standoff over the South China Sea thus has many levels of complexity. It is not simply about one body of water, or a single boundary. As Tommy Koh, a senior Singaporean diplomat who led negotiations to create the United Nations Convention on the Law of the Sea, told me, “the South China Sea is about law, power, and resources, and about history.”

That history is haunted in particular by four ghosts, long-departed men from centuries past whose shadows fall across the South China Sea, their legacies shaping the deepening rivalry in the region; historical figures whose lives and work have framed the disputes about sovereignty and freedom of navigation, the competition of navies, as well as war and its costs.

During the writing of my book, The New Map, I began thinking about these men. When I was speaking on the challenges of globalization and international commerce at the U.S. Naval War College in Newport, Rhode Island, the commanders of virtually all the world’s navies were there, a galaxy of admirals, all resplendent in their dress uniforms. Among them was Admiral Wu Shengli, the head of China’s navy at the time and the man who was driving its expansion to compete with the American Navy. By then the South China Sea had already become a center of contention. Wu sat in the center of the audience, in the fifth or sixth row, his gaze unwavering throughout.

That was when I started seeing ghosts: that of China’s greatest seafarer, a predecessor to Wu; of the Dutch lawyer who penned the legal brief that now underpins the American argument against China’s claims; of the American admiral whose philosophies offered a foundation for both the U.S. Navy and Chinese maritime expansionism; and of the British writer who argued that the costs of conflict were too high, even for those who would be victorious.

For modern China, claims to the South China Sea center around what is called the “nine-dash line”—literal dashes that, on the Chinese map, hug the coasts of other nations and encompass 90 percent of the waters of the South China Sea. Derived from a map drawn by a Chinese cartographer in 1936 in response to what Beijing calls the “century of humiliation,” the nine-dash line is, according to Shan Zhiqiang, the former editor of China’s National Geography magazine, “now deeply engraved in the hearts and minds of the Chinese people.” Chinese schoolchildren have for decades been taught that their country’s border extends more than a thousand miles to the coast of Malaysia. Beijing’s claims are bolstered by military bases that it has built in recent years on tiny islands and on 3,200 acres of reclaimed land scattered in the middle of the sea.

Beijing bases its claim of “indisputable sovereignty” upon history—that, as an official position paper put it, “Chinese activities in the South China Sea date back to over two thousand years ago.” These “historic claims,” in the words of a Chinese government think tank, have “a foundation in international law, including the customary law of discovery, occupation, and historic title.”

The U.S. replies that, under international law, the South China Sea is an open water—what is often called “Asia’s maritime commons”—for all nations, a view shared by the countries that border its waters, as well as by Australia, Britain, and Japan. As such, says the U.S. State Department, China “has no legal grounds” for its South China claims and “no coherent legal basis” for the nine-dash line. “China’s maritime claims,” a U.S. government policy paper argued this year, “pose the greatest threat to the freedom of the seas in modern times.”