By the first centuries A.D., the Chinese had some knowledge of the winds and currents of the Pacific, though they thought the waters of the four oceans around them emptied into a great whirlwind or abyss from which no traveler could return. The astronomer Zhang Heng believed the earth floated in space like a yolk in the albumen of an egg, [19] thus understanding even at this early date that the world was round.

What, then, became of the Daoist priest and the thousands of young men and women who went looking for the herbs of immortality? One theory is that the expeditions landed in Japan and that Jimmu Tenno, the founder of the Japanese empire, was in fact Xu Fu. Another is that the Daoists succeeded in crossing the Pacific, landing in Central America during the rise of the Mayan and perhaps having some perceptible, but small influence on their civilization. [20] Many have remarked at the similarity between Chinese characters and the square-shaped Mayan glyphs, and the astonishing resemblance of the Chinese and Mayan calendars with their complicated, intercepting cycles of days and years.

[...]

The Chinese spun their own tales, one of which suggests that Buddhist monks reached the shores of America in the fifth century A.D. The story, as recorded in the Liang shu (History of the Liang dynasty), describes the voyage of Hui Shen and five Afghan monks to a strange place called Fusang guo32—the Country of the Extreme East—that seems to bear a strong resemblance to Mayan Mexico. Hui Shen said he found people there who made cloth and paper from bark and wrote with characters. Like the emperor of China, the king of this place, he reported, was preceded and followed by drummers and heralds, and he changed the colors of his robe (as did the Son of Heaven) in accordance with a ten-year cycle. Like China, Fusang guo had a severe judicial system in which not only a criminal but also his children and grandchildren were punished.

It would be easy to dismiss the possibility that Hui Shen visited Central America if it were not for a strong influx of Buddhist and Hindu elements that appear in Mayan art at this time. Suddenly, Mayan bas-relief figures are depicted on lotus thrones, sitting cross-legged like meditating Buddhas. There also appear multiheaded deities similar to the multiheaded gods of India. Moreover, the detailed bas-reliefs at Copán, Honduras, show priests dressed in diamond-patterned ceremonial robes that bear an astonishing resemblance to traditional Tibetan Buddhist robes [33]. Stone statuary at Xculoc, Mexico, shows a distinctive hand gesture [34]—right hand lowered, palm out; left hand raised, palm out—that appears to be a classic Buddhist stance called shi yuan wu wei, meaning “the granting of a wish.” Some outside Buddhist-Hindu influence on Mayan civilization [35] seems likely, whether it is attributable to Hui Shen and his Buddhist companions or to other Asian seafarers. This is thought to have been the last period of contact between Asia and the Americas before the arrival of Columbus.

“In former times [the people of Fusang guo] knew nothing of the Buddhist religion, but in the second year of Da Ming of the Song dynasty [485 A.D.], five monks from Chipin [Kabul, Afghanistan] traveled by ship to that country. They propagated Buddhist doctrines, circulated scriptures and drawings, and advised the people to relinquish worldly attachments. As a result, the customs of Fusang changed.

—Liang shu, seventh century A.D.

from When China Ruled the Seas by Louise Levathes