I'm just finishing a book called Columbus was Chinese, by Hans Breuer; originally published in German in 1970, then in English in 1972.
Much of the book deals with scientific and technological discoveries that were made in China before there is any record of them in Europe. Chapter 1, Novae and Pulsars--there was genuine astronomy in China, studied alongside astrology, albeit with a certain amount of secrecy, as early as 1500 B.C.; star charts can be dated back to 400 B.C. Charts from the fourth century A.D. are "amazingly modern," and quite different in orientation from Greek ones that can be traced to Hipparchus (c. 190-125 B.C.). Only by means of very recent technology is it possible to confirm that Chinese scholars identified a supernova in 1054 A.D. Arab astronomers at this time seem to have missed it, although their science was in some ways highly developed. Modern astronomers have been able to confirm the timing of Halley's comet from Chinese chronicles dated 240 B.C. In the West, for many centuries, adherence to Ptolemy's theories literally prevented anyone from confirming exact observations of the skies. "What ought not be simply cannot be."
Chapter 2, Abacus etc. Chapter 3, maps. Chapter 4, the Great Wall. Chapter 5, the oldest seismograph. Chapter 6, the compass. On this: there has been some awareness of magnetism since pre-historic times. The first written "qualitative" account of a magnet comes to us from Thales of Miletus in the sixth century B.C., but three hundred years later a Chinese source not only gives a similar description, but a "quantitative measure of the strength of magnets." Within a few hundred years lodestones were in use in China. "... the Chinese can undoubtedly claim the glory of discovering the compass [as well as] ... the declination of the needle, that it systematically declined from the astronomical meridian. That is highly interesting since this discovery was attributed to Columbus, which would date it 400 years later." The compass was used in navigation in China no later than the tenth century, but was not known in Europe until two hundred years later.
Chapter 7: Kites, Rotors, Balloons, and Parachutes. Chapter 8: Paper. Chapter 9: The Black Art (printing). On printing, the Chinese perfected block printing, but probably never developed movable type. Once Gutenberg got going, he greatly surpassed even the movable type of Korea. On some discoveries, once Europe had a start, it went much farther than China as part of modernity. But credit for the start still goes to China.
Chapter 10: Paper money. Chapter 11: Gunpowder and Cannons. Fascinating stuff, but I'll mention only a few points. The Chinese used a very crude gunpowder for fireworks on special days. They found some military applications, such as using gunpowder to ignite some kind of petroleum from the ground so as to make a flame-thrower. There were also a few cases of a massive bomb or mine being exploded. Once Europeans had the idea, "Chinese ordnance fell hopelessly behind compared to the development that took place among the Europeans and Arabs. ... Granulated black powder (1520) enclosed more air and thereby increased its eficiency. ... Time fuses were invented as early as 1585."
Chapter 12: Silk and the Silk Road. (Ancient and historical contacts between China and Europe).
Chapter 13: the piece de resistance: "Columbus was Chinese." This is not about the possibility that a specific Chinese naval explorer might have reached the Americas a few decades before Columbus. Instead Breuer identifies signs that Chinese and other Asian people, products or ideas reached the Americas long before--probably centuries before. He focusses on three groups of "First Nations" and their customs "that simply will not fit into [the] uniform image [of First Nations]: the peoples of the Northwest Coast, now in Canada; the Olmecs of the narrow strip at the south of Mexico; and the Chavins of the north Peruvian Andes.
For the Northwest "Indians," Breuer says the Tlingit, Haida and Chimmesyan are "foremost". They have a strict caste system, with the nobles chiefly preoccupied with acquiring and maintaining prestige; double canoes that can go out to sea; totem poles; and figurative art that displays bilateral representation. "... their culture is unique on the American continent; we find nothing resembling it either in North, Central, or South America."
Of the Olmecs (earliest finds about the time of the birth of Christ) Breuer says rather rudely: "Since the turn of the century signs have multiplied indicating that once men must have lived on the plains of Tehuantepec who would have had little in common with the Indians now vegetating there." Unusual features include "artistic jade sculptures," "temples," "steles," and "tombs." "The form of the pyramids and steles greatly resembles that of the Mayas and the Aztecs, yet nowhere in America does this sculpture have a counterpart." According to archeological finds, "the Olmec culture appeared quite suddenly and at a level of perfection,without any preliminary stages." Some of the artifacts actually decline in quality after their initial appearance. Olmec influence can be found in all later Central American cultures, especially the Mayas and the Zapotecs.
Of the Chavins (sudden appearance of artifacts about tenth or ninth century B.C.), Breuer says "they were master goldsmiths," they "perfectly mastered the art of weaving," and in other ways they stood out from nearby groups.
Starting on p. 228 Breuer addresses the debate betwen "isolationists," who say all the First Nations of the Americas are derived from one immigration, and "diffusionists," who say there has been some penetration from time to time by other groups and cultures, who were diffused or dispersed in such a way as to reach the Americas, and became somewhat isolated elements there. The "lost-wax" process of casting metal appeared in Peru, quite suddenly, in 4 B.C.; the development of this process took 1500 years in Mesopotamia (today's Iraq) and the Indus valley. Even pottery-making takes more time to develop than would apparently have been available. Jade figurines, the calendar system of the Olmecs, and other things are hard for the isolationists to explain. "The Olmecs exhibit a mastery of figural representation that is still unmatched in all of America."
After considering several possibilities, Breuer suggests it is at least possible that a few strangers might have made it all the way to the Americas from China, sailing across the Pacific. Partly this argument overlaps with the work of Thor Heyerdahl, showing that fairly "primitive" people could travel vast distances by water. Another small piece of evidence: "between 1800 and 1950 alone more than fifty ships, partly Japanese, partly Chinese junks, were driven onto the coast of California." Breuer admits that even if there is a match between a particular time in China and some of the artifacts in the Americas, there is no perfect match.
Breuer discusses specific plant foods. The coconut clearly was in Asia before it was in the Americas, and seems to have grown in the Americas before Columbus. A single coconut probably could not have made the trip unless it was carried in some kind of boat. The sweet potato, conversely, started in Central America, but it reached Polynesia and from there, Asia, before there were Europeans in the Americas. "The only remaining possibility is that the inhabitants of Polynesia reached the coasts of Central America and took sweet potatoes on board for the return voyage." Generally speaking, there are more botanical species on the Pacific Islands the farther west we go; this provides evidence that many of them began in Asia.
This is already a long post: is it possible that at least a few ethnically and culturally distinct people managed to plant themselves in America, which was otherwise settled by a relatively uniform group of First Nations? A 2008 paper, based on genetic studies, suggests that almost all of the genetic material of surviving First Nations suggests a common ancestry in one migration across what is now the Bering Strait. After offering their explanation, the authors say: "A similar explanation may be used to account for the existence of other similarly rare haplogroups in the Americas, such as the “cayapa” subhaplogroup D,69 as well as the distribution of some rare Y chromosome haplogroups,70 without the need to postulate independent colonization events."
But there remains a possibility of other colonization events, and this genetic study is based on surviving genes; what if some of the imported groups were wiped out by conquest or disease, to the last man, woman and child?
Wikipedia at least briefly entertains the possibility of "foreign" migration in the case of the Olmecs:
The flat-faced, thick-lipped characteristics of the [sculptured] heads have caused some debate due to their apparent resemblance to African facial characteristics. Based on this comparison, some have insisted that the Olmecs were Africans who had emigrated to the New World. However, claims of pre-Columbian contacts with Africa are rejected by the vast majority of archeologists and other Mesoamerican scholars. Explanations for the facial features of the colossal heads include the possibility that the heads were carved in this manner due to the shallow space allowed on the basalt boulders. Others note that in addition to the broad noses and thick lips, the heads have the Asian eye-fold, and that all these characteristics can still be found in modern Mesoamerican Indians. To support this, in the 1940s artist/art historian Miguel Covarrubias published a series of photos of Olmec artworks and of the faces of modern Mexican Indians with very similar facial characteristics. In addition, the African origin hypothesis assumes that Olmec carving was intended to be realistic, an assumption that is hard to justify given the full corpus of representation in Olmec carving.