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Zheng He, a eunuch Muslim, takes his first of seven voyages for China, under the Yonglu Emporer, wanting to earn respect from other countries that brought back tributes, and astound the world with the ships', fleets', and crews' magnificent sizes. He does.
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Prince Henry "the Navigator", a very enthusiastic patron of Portuguese exploration, establishes a navigation school on Portugal's southwestern coast to help exploration-associated people fine-tune their trade, a trade like mapmaking, shipbuilding, or being a sea captain. Many associates of his school go on to lead important Portuguese expeditions.
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Although China's isolation policy allows government-conducted trade with only three ports, to keep the outside influence to a minimum, many merchants smuggle things like silk and porcelain to Europeans, who pay with mostly silver. Certain industries grow larger, and some European traders bring Christianity to China, which many Chinese oppose.
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Competition among Portugal and Spain for Indian Ocean trading monopoly drove Christopher Columbus, a Spainard, to set out across the Atlantic to find a new route to Asia. Instead of finding Asia, though, he finds a Carribean Island, and Europeans find America. Then the colonies, the Revolutionary War, and later, us.
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Asian trading competition, sparked by Columbus's voyage, grows more tesnion between Spain and Portugal. To peacekeep, Pope Alexander VI steps in and draws the Line of Demarcation, a line that gives most of the Americas to Spain, and a small part (part of which would become Brazil) to Portugal, which the two countries honor in the Treaty of Tordesillas. Spain and Porugal go on to have a major cultural effect on America.
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Although Portuguese Bartolomeu Dias had rounded the tip of Africa in a storm a decade prior, Vasco de Gama makes the first voyage all the way to a port called Calicut in India, looking to grow richer and spread Christianity. Soon, Portugal is the monopoly of Indian Ocean trade, and grows richer.
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After Toyotomi Hideyoshi dies, in 1598, Tokugawa Iesayu, unifies Japan, stopping powerful samurai from rebelling, to create a more centralized government in Japan, and goes on to be the first ruler (or shogun) of the Tokugawa Shogunate, which will last until 1867. The Tokugawa Shogunate's military-induced stability brings a blossoming of Japanese culture.
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The Manchus invade the weakening Ming China, and Kangxi, the first Qing Emporer, rules for 60 years. He gains trust from the Chinese by sticking to Confucian ideas and traditional Chinese values, and starts a dynasty that will be China's longest (250 years), last, and largest. China sticks to most of its traditional principles, but when the dynasty ends, in 1911, it is pretty corrupt from rebellions, bad harvests, and an unresponsive government.