This question can't be properly answered without a considerable amount of history, really on both sides. What follows is a very, very short abridged version of some of the relevant history, focusing on events that really impacted relative wealth. In short, from the mid-19th century on, China was heavily war-torn, and through much of that time, under the heel first of foreign powers. Then it suffered the economically ruinous policies of Mao.
If you go back to the year of the signing of the American Declaration of Independence you'll see that it roughly coincides with the apex of Imperial China's wealth and power. China's balance of trade with the rest of the world was such that something like two-thirds of all the world's silver coin had, by 1776, flowed into China. China also had more printed books at that time than the rest of the world combined. It was an enormous empire, with land area considerably larger than the current People's Republic of China and a population of roughly 300 million.
At that time, China was ruled not by Han Chinese (the majority ethnicity of China then as now), but by Manchus, a Tungusic people who had originally come from the woodlands, mountains, and high steppeland of what is now Manchuria and the borders of North Korea. They had conquered China in 1644, taking advantage of the very recent collapse of the Ming Dynasty, which had ruled China from 1368 to 1644, after the Ming had been overthrown only months earlier by internal rebellion. The Manchus established a Chinese-style dynasty called the Qing, and ruled very much in the Chinese style, with the same Confucian civil service system and most institutions more or less intact. Indeed they very quickly became quite sinicized, and by the time of the American Revolution, the sitting emperor, Qianlong, was an adept stylist in Chinese, a connoisseur of Chinese art.
This "Son of Heaven" had every reason to believe that he ruled a true "Middle Kingdom," unparalleled in wealth, in power, in prestige, in culture. Although some of his predecessors had entertained and sometimes even befriended foreign visitors, some of them (certain Jesuit missionaries, especially), and were aware of the advances some of their countries had made in cartography, in astronomy, and in the manufacture of, say, clocks and other mechanical devices, they saw these things as little better than clever toys. They had no idea whatsoever of the system of science the undergirded these "clever toys." And they had no real desire to trade with the "seafaring barbarians" who came to China from countries like Great Britain. Lord Macartney, who came to China in 1792 in the hopes of securing trade relations during Qianlong's reign, was rebuffed by the Qing Emperor and told to go home.
And so it was that toward the end of Qianlong's long (sixty year!) reign—and mind you, China was already experiencing certain pressures as a result of population, rot in the bureaucracy, millenarian uprisings like the White Lotus Rebellion—they were wholly unprepared for the brutal encounter that was coming next.
China had of course been selling absurd amounts of tea, of porcelain, and silk—but mostly tea—for which it would only accept payment in silver. In the late 18th century, British merchants began introducing opium, grown in their Indian colony and shipped to Canton, the city to which trade was restricted. This proved to be the one good for which there was any demand, and by the 1820s the balance of payments had shifted radically and opium addicts in China numbered in the millions. When the Chinese court eventually dispatched one of its most attained courtly gentleman scholars, Lin Zexu, to end the opium problem, they had no idea that Britain would react with such force. They were unaware that British ships could move freely in the shallow waters of the Pearl River Delta; that their guns had such range and such accuracy; that their fortifications would be basically useless against the assault that followed in the Opium War of 1840. China had to sue for peace, signing the Treaty of Nanjing—the first of several "Unequal Treaties" opening several treaty ports to trade, establishing extraterritorial legal status for foreigners in China, and making China if not into a full-blown colony than at least into a "semi-colonial" state, as Mao would have put it.
The century that followed the Opium War saw no semblance of peace. From 1850 to 1863, China was torn apart by the biggest civil war probably in world history, the Taiping Rebellion, in which an estimated 20 to 30 million Chinese lost their lives when a failed scholar named Hong Xiuquan, believing himself to be the brother of Christ and son of God, commanded to expel the Manchu "demons," went at it with gusto and a fuck-ton of followers. Concurrently, a kind of brigand-cum-rebel force called the Nian raised hell in the North China Plain, in Jiangsu, Shandong, Henan and southern Hebei provinces. A second Opium War was fought in 1860, this time resulting in the utter destruction of the gorgeous Old Summer Palace in northern Beijing, which was sacked by French and English soldiers. The Qing court had to flee, only to return under more humiliating conditions.
Still no breathing room and no breaks. Chinese intellectuals of the 1860s and 70s were stuck on this idea of "self-strengthening" through appending Western technology onto a basically Chinese corpus of culture and though. Didn't exactly work. France fought a war with China; Japan fought a war (1894-95) during which it was able to claim Taiwan, which it ruled until the surrender in 1945. After the 1894-95 war was settled by the Treaty of Shimonoseki, other Imperial powers asked themselves, "Well, if Japan gets to carve off a piece of China, shouldn't we be able to as well?" There followed a "scramble for concessions" during which Chinese truly believed their nation to be about to be "carved up like a melon."
Then came the disaster of the Boxer Rebellion. Beginning as a rurally-based anti-foreign cult of sorts convinced that their exercises rendered them impervious to bullets, they began attacking missions and other outposts of foreign presence. The Qing court at first sought to suppress them, but soon decided they could be used to help oust the colonial presence in China. The Boxers laid siege to the foreign legation quarter in Beijing for over three months. The results were catastrophic: Eight allied foreign armies came to the relief of the legation quarter, and afterward imposed onerous reparation demands on the Qing court.
At last the court began to get serious about reforms, but it was too little and too late, and the reforms—and this is really the lesson in Tocqueville's Le Ancien Regime—actually hastened the end of the regime by emboldening not just reformers but revolutionaries like Sun Yat-sen and his Alliance Society (Tongmenhui), which he had formed in exile in Japan. The October 10 revolution of 1911 ended up deposing the last Qing monarch, but the so-called Republic of China he founded was very short-lived. The real power of the day was an old Qing general named Yuan Shikai, who made a deal, essentially at gunpoint, to become the first "provisional" president of China. His years in power saw two more revolutions against him. Then in 1916, his hold already shaky, Yuan made the dumb move of deciding to become emperor (having believed what his Columbia political scientist adviser, Frank Goodnow, told him about the innate desire of the Chinese people for an emperor), and declared a new dynasty. Fortunately he died shortly thereafter.
But on his death China fell into pieces as contending militarists—the Warlords, as they were called—each claimed territory and fought to control Beijing as a symbol of a legitimacy that none in fact possessed. The number of battles between warlords and their shifting factional alliances between 1916 and 1928 can be counted in the thousands, the number of deaths can be reckoned in the hundreds of thousands if not in the millions.
The Chinese Nationalist Party, the Kuomintang, finally managed to recapture parts of China from various warlords in the late 1920s, marching north from their power base in Guangdong province on a "Northern Expedition," taking Shanghai and Nanjing and setting up a capital in the latter city. This ushered in one of China's few periods of relative peace during the century following the Opium War, the Nanjing Decade from 1928 to the Japanese invasion of 1937. But even then, the Kuomintang leader Chiang Kai-shek only ruled a very small part of China; and things were hardly really peaceful. The Nanjing Decade actually started off with a brutal"White Terror" in which Chiang purged the Communists, who had been allied with the Nationalists in efforts to take back the country from the warlords. He slaughtered them ruthlessly, employing his Green Gang gangster cronies in Shanghai for much of the dirty work. And then he set out to exterminate the Communists: Chiang launched campaign after campaign (five in all) to encircle and strangle the Communists in their Jiangxi stronghold, the Jiangxi Soviet. It was during the last push that the Communists decided to hightail it out of Jiangxi and head, after a long and tortuous path across thousands of miles, the Nationalists battling them much of the way, to the loess caves of arid northern Shaanxi province—the famous "Long March."
Chiang probably would have wiped them out there had it not been for the Japanese invasion. In the late 1920s, Japanese rightwing militarists were already clamoring for the creation of a land empire in Chinese territory, and in 1931, seized Manchuria—China's three norhteastern provinces—renaming it "Manchukuo" and installing as its head the deposed last Qing emperor, "Henry" Pu Yi. Chiang refused to fight them—"The Japanese are a disease of the skin; the Communists are a disease of the heart," he said—and eventually they began a full war with China in 1937.
The war lasted until 1945, the Chinese government pushed into Chongqing in the southwestern province of Sichuan, barely hanging on. And soon after the Japanese surrender in August 1945, there was of course the unfinished business between the Nationalists and Communists, so more war was inevitable, despite the best efforts of General Marshall.
Things don't get any better after the Communist victory, or at least not for long. Mao's zany collectivization scheme, which he began to put into effect in the mid-1950s, was an abject economic disaster, but it was nothing compared to the "Great Leap Forward," which brought on one of history's most horrific famines, with upwards of 30 million deaths according to fairly conservative estimates. A brief respite from this during the period 1961 to 1965 saw relatively sensible leaders like Liu Shaoqi and Deng Xiaoping try at least to run a rational command economy. But Mao was back with a vengeance from 1966, when he launched the Great Proletarian Cultural Revolution, and threw the country back into virtual anarchy as he encouraged people to tear down all structures of authority: in the school, in the university, in the workplace, within the Party, you name it. Only thing that remained largely unscathed was the Army, which was able to restore some semblance of order.
And so "normal life" at which there's any reasonable basis for comparison to the U.S. doesn't even begin in China really until Mao's death, or not until the end of 1978 with the inauguration of reform. The setbacks we're talking about are mindboggling. Sure, the US had a few bad episodes during its what, 237 years of life to date: There was the Civil War of course. Any other major wars fought on American soil? Nope. American deaths numbered in the 10s of millions? Nope. Revolutionary overthrows? Nope. Massive political purges or terrors? McCathyism at its worst paled by comparison to Mao's Anti-Rightist Movement.
America started with a virgin, resource-rich continent with vast oceans to either side and an indigenous population that had no resistance to common old world diseases like smallpox. And where they weren't dying naturally, infected blankets—or Gatling guns—helped. Its late entries into two massive World Wars only increased its relative economic might. Remember, China has between one-fifth and one-sixth of the world's population, but only about seven percent of the world's arable land. Just one valley in America, the San Joaquin Valley of Central California, produces something like one-eighth of America's agricultural value.
America's "Cultural Revolution" of the 1960s led to a true blossoming of culture. The litany of cultural changes that America went through between 1949 and 1979—the years between the founding of the PRC and the beginning of the Reform period in China—are simply incomparable to China. China went backward culturally during this period. And in America? Be-bop, the Beats, the Civil Rights Movement, Lenny Bruce, Catcher in the Rye, Elvis, the Beatles, the whole British Invasion, Hendrix, Timothy Leary, LSD, the Pill, Philip Roth, Norman Mailer, Raging Bull, The Godfather I and II, the Anti War Movement, Watergate, disco, cocaine, Punk rock, and Saturday Night Life. In China, the most revolutionary thing was a Taiwan pop singer who named Theresa Teng whose cassette tapes you could maybe get if you were lucky by 1979.
You were inspired by Outliers to pose this question. The odd confluence of factors that combined to create the Industrial Revolution in England (and later, other parts of Western Europe and North America) actually makes Europre and the west the historical outlier. People who ask the question "Why didn't China experience the Industrial Revolution" are actually kind of asking the wrong question. The question is, why did England?
Obviously this question is worth a book. Looking forward to reading other answers to it.
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