Scientific American have posted the first in a series of articles on the Needham Question. Its namesake, Joseph Needham, observed that through the 1st and 17th centuries Chinese science and technology flourished. Its inventions included paper, the printing press, the magnetic compass, and gunpowder. But, then, quite inexplicably, progress stopped.
In The Grand Titration, Needham asks:
Why did modern science, the mathematization of hypotheses about Nature, with all its implications for advanced technology, take its meteoric rise only in the West at the time of Galileo? This is the most obvious question which many have asked but few have answered.
In the column, Gorelik extends the problem:
Most important is not why Europe was the first to launch the modern physics—somebody has to be the first—but why for so long nobody joined the modern physics beyond Europe. European culture borrowed important innovations from China, India, and Islamic world like paper, Hindu-Arabic numerals, and algebra. However the greatest Western innovation of the modern physics did not transfer South-East for centuries.
The traditional answer is twofold. Firstly, Chinese cultural and religious values tripped-up development. Wisegeek summarises this nicely:
[...] the answer had to do most with the way Confucianism and Taoism promoted a way of life incompatible with huge scientific advances. Emphasis on wholeness in community thinking and respect to elders meant that children and even college students could not question teachers. A desire to maintain strong cultural identity discouraged new developments in favor of keeping a traditional way of doing things. To Needham, China’s culture and its philosophy and religion just was not interested in the high paced dramatic ahege of discovery in the West.
Secondly, early capitalism in the West encouraged competition and individualism, which were conducive to experimentation and inventiveness. And, a robust capitalist infrastructure meant that the West could coordinate large-scale scientific and industrial projects. Timur Kuran writes:
The regions that failed to keep up with Europe could not match the West's economic infrastructure. Most important, they failed to develop institutions for pooling labor and capital on a large scale and to develop sustainable organizations capable of reallocating resources efficiently. In the Middle East, religion, and culture more broadly, mattered, but not for the cosmological reasons that Needham might have thought. Rather than Islam's supposed conservatism, lack of curiosity about the natural world, or unwillingness to learn from foreigners, it was Islam's inheritance and marriage rules that created the stumbling block. These rules fragmented capital, blocking the establishment of large and durable private enterprises. Meanwhile, in South Asia, Hinduism hindered large-scale, impersonal cooperation by encouraging families to hold capital within family enterprises.
Otherwise, Simon Winchester has a video lecture online. There's a snippet below:
And, BBC Radio 4 hosted a discussion on the question that is available for listening.
Addition: A number of alternative explanations have been offered. Nathan Sivin asserts that China only ever demonstrated technological success, and not scientific success. Mark Elvin claims that explosive Chinese population growth in the 17th Century stretched the country to breaking point, meaning it did not have the resources to sponsor an industrial revolution. And, finally, Roger Hart picks out two further explanations:
Alfred Bloom asserted that the Chinese language had inhibited the ability of the Chinese to think theoretically. Robert Hartwell argued that the major impediment was the absence of the formal logical system embodied in Euclidean geometry.