To my essay Western Civilization and Socratic Dialogue, Dymphna of the Gates of Vienna blog wrote a comment about Greek vs. Chinese ways of thinking. This is an interesting subject which I will explore further here, with an emphasis on mathematical astronomy. The Danish nobleman and astronomer Tycho Brahe (1546–1601), born in Scania or Skåne in southern Sweden, then a part of the Kingdom of Denmark, from 1600 until his death in 1601 was assisted by theGerman mathematical astronomer Johannes Kepler (1571–1630), who published his Astronomia nova in 1609 with calculations of the elliptical orbit of Mars based on Brahe's careful observations. The English scholar Sir Isaac Newton (1642–1726) has no equal in the history of science, with the possible exception of Albert Einstein. Yet even he did not work in isolation.

Here is The Oxford Guide to the History of Physics and Astronomy, page 227:

"In 1679, Newton learned of Robert Hooke's idea that orbital or curved motion could be explained by a combination of a linear inertial component along the orbit's tangent and a continual falling inward toward the center. Newton wrote that he had never before heard of this 'hypothesis.' But he perceived a connection between Hooke's suggestion and Johannes Kepler's law of areas, and showed that they implied that the tendency toward the center in planetary elliptical orbits must vary as the inverse square of the distance from the Sun. He informed no one about this great breakthrough. In 1684 Newton received a visit from Edmond Halley, who asked for help in solving a problem that had stumped everyone in London: the force that produces planetary elliptical orbits. Newton replied that he had already solved it. He wrote up his solution in a little tract called De motu. While revising and expanding it, he discovered that the same force that keeps the planets in orbit must cause perturbations in the orbital motions of other planets, the key to the great principle and law of universal gravitation….In 1687 he published his resulting masterpiece, Philosophiae naturalis principia mathematica (Mathematical Principles of Natural Philosophy)."

Kepler's laws, which helped pave the way for Newton's Principia, were developed in the early 1600s based on Brahe's naked-eye observations. Just a few decades earlier, Copernicus had placed the Sun at the center of the Solar System instead of the Earth. Ptolemaic astronomy had thus been superseded in Europe even before the introduction of the telescope. It is interesting to contrast this with Muslims, who had the same Ptolemaic and Greek starting point during the Middle Ages, yet nevertheless did not produce a similar breakthrough.

Could something like the Principia have been produced in China? Here is Science and Technology in World History by James E. McClellan and Harold Dorn, page 132-133:

"Although weak in astronomical theory, given the charge to search for heavenly omens, Chinese astronomers became acute observers….who produced systematic star charts and catalogues. Chinese astronomers recorded 1,600 observations of solar and lunar eclipses from 720 BCE, and developed a limited ability to predict eclipses. They registered seventy-five novas and supernovas (or 'guest' stars) between 352 BCE and 1604 CE, including the exploding star of 1054 (now the Crab Nebula), visible even in the daytime but apparently not noticed by Islamic or European astronomers. With comets a portent of disaster, Chinese astronomers carefully logged twenty-two centuries of cometary observations from 613 BCE to 1621 CE, including the viewing of Halley's comet every 76 years from 240 BCE. Observations of sunspots (observed through dust storms) date from 28 BCE. Chinese astronomers knew the 26,000-year cycle of the precession of the equinoxes. Like the astronomers of the other Eastern civilizations, but unlike the Greeks, they did not develop explanatory models for planetary motion. They mastered planetary periods without speculating about orbits. Government officials also systematically collected weather data."

The comet we know as Halley's Comet had been spotted many times before the great English astronomer Edmond Halley (1656–1742), but it was not recognized as a periodic comet until eighteenth century Europe, which is significant. The Chinese had apparently never calculated the orbits of either Halley's Comet or other comets which they had observed. They had a large mass of observational data, yet never used it to deduct mathematical theories about the movement of planets and comets similar to what Kepler, Newton and others did in Europe. Newton's Principia was written a few generations after the introduction of the telescope, which makes it seductively simple to believe that the theory of universal gravity was somehow the logical conclusion of telescopic astronomy. Yet this is not at all the case.

What would have happened if the telescope had been invented in China? Would we then have had a Chinese Newton? This is impossible to say for certain, of course, but I doubt it. Chinese culture never placed much emphasis on law, either in human form, as in secular Roman law, natural law or divine law. If the Chinese had invented the telescope, I suspect they would have used it to study comets, craters on the Moon etc., which would clearly have been valuable, no doubt. Any culture that used telescopes would have generated new knowledge with the device, but not necessarily a law of universal gravity. McClellan and Dorn, page 259:

"Newton's celestial mechanics hinges on the case of the earth's moon. This case and the case of the great comet of 1680 were the only ones that Newton used to back up his celestial mechanics, for they were the only instances where he had adequate data. With regard to the moon, Newton knew the rough distance between it and the earth (60 Earth radii). He knew the time of its orbit (one month). From that he could calculate the force holding the moon in orbit. In an elegant bit of calculation, using Galileo's law of falling bodies, Newton demonstrated conclusively that the force responsible for the fall of bodies at the surface of the earth – the earth's gravity – is the very same force holding the moon in its orbit and that gravity varies inversely as the square of the distance from the center of the earth. In proving this one exquisite caseNewton united the heavens and the earth and closed the door on now-stale cosmological debates going back to Copernicus and Aristotle. In proving this and the comet case, Newton simultaneously opened the door on a whole new world of problems to solve."

In his excellent book Cosmos, John North points out that in China, where astronomy was intimately connected with government and civil administration, interest in cosmological matters was not markedly scientific in the Western sense of the word and did not develop any great deductive system of a character such as we meet in Aristotle or Ptolemy. Page 136:

"The great scholar we know as Confucius (551 BC-478 BC) did nothing to help this situation – if in fact it needed help. Primarily a political reformer who wished to ensure that the human world mirrored the harmony of the natural world, he wrote a chapter on their relation, but it was soon lost, and a number of stories told of him give him a reputation for having no great interest in the heavens as such….The all-pervading Chinese view of nature as animistic, as inhabited by spirits or souls, gave to their astronomy a character not unknown in the West, but at a scholarly level made it markedly less well structured. At a concrete level, we come across such Chinese doctrines as that there is a cock in the Sun and a hare in the Moon – the hare sitting under a tree, pounding medicines in a mortar, and so forth. At a more abstract level there is the notorious all-encompassing doctrine of the yin and the yang, a form of cosmology that is to Aristotelian thinking as yin is to yang."

He adds on page 139 that "Unlike Platonic and Aristotelian thought, Chinese thought was not overtly philosophical, but rather, it was historical. Joseph Needham, a well-known authority on the history of science in China, has suggested that the reason for this is that Chinese religion had no lawgiver in human guise, so that the Chinese did not naturally think in terms of laws of nature."

Naturally occurring regularities and phenomena could be observed, of course, but the Chinese did not generally deduct universal natural laws from them, possibly because their view of nature was that reality is too subtle to be encoded in general, mathematical principles. In European astronomy phenomena such as comets, novae and sunspots that did not readily lend themselves to treatment in terms of laws were taken far less seriously than those that were. The history-conscious Chinese, on the other hand, kept detailed and plentiful records of all such phenomena, records which still remain a valuable source of astronomical information.

Su Sung's (1020-1101 AD) astronomical water clock was an impressive mechanical device by eleventh century standards, and his work included a star map based on a new survey of the heavens, the oldest printed star map ever recorded. The Chinese could clearly produce talented individuals, but their work was often not followed up. The Imperial bureaucracy was hampered by many obstacles to the free and unfettered pursuit of scientific knowledge, especially due to excessive secrecy and regulation in the study of mathematics and astronomy. By making this study a state secret, Chinese authorities drastically reduced the number of scholars who could, legitimately or otherwise, study astronomy. This restriction greatly reduced the availability of the best and latest astronomical instruments and observational data. The Rise of Early Modern Science, second edition, by Toby E. Huff, page 313:

"The fact remains that virtually every move made by the astronomical staff had to be approved by the emperor before anything could be done, before modifications in instrumentation or traditional recoding procedures could be put into effect. It is not surprising, therefore, that despite the existence of a bureau of astronomers staffed by superior Muslim astronomers (since 1368), Arab astronomy (based as it was on Euclid and Ptolemy) had no major impact on Chinese astronomy, so that three hundred years later when the Jesuits arrived in China, it appeared that Chinese astronomy had never had any contact with Euclid's geometry and Ptolemy's Almagest. Moreover, contrary to Needham's arguments, more recent students of Chinese astronomy suggest that Chinese astronomy was perhaps not as advanced as Needham suggested and that 'Chinese astronomers, many of them brilliant men by any standards, continued to think in flat-earth terms until the seventeenth century.' If we consider the study of mathematics, in which the metaphysical implications of abstract thought may be less obvious to outsiders and which may therefore give scholars more freedom of thought, we encounter an institutional structure equally detrimental to the advancement of science."

Astronomy in the Islamic world stagnated and never fully managed to leave behind its Ptolemaic structure, as Europeans eventually did, but Muslims were familiar with Greek knowledge and geometry which the Chinese apparently failed to adopt during the Mongol period. The sphericity of the Earth had been known to the ancient Greeks since at least the time of Aristotle in the fourth century BC and was never seriously questioned among those who were influenced by Greek knowledge in the Middle East, in Europe and to some extent in India. The myth that medieval European scholars believed in a flat Earth is of modern origin.

Mesopotamian mathematical astronomy reached India during the Persian conquests of northwest India by the fifth century BC, along with alphabetic writing systems. Contact with Greek astronomy came after Alexander the Great's conquests of the same region and through trade contact between Romans and western India during the first and second centuries AD. This was the period after Hipparchus but before Ptolemy, so the Greek astronomy used in India was not that of Ptolemy. Indians were clearly influenced by spherical trigonometry in the Greek fashion as well as by Babylonian material, but the Indian tradition was far from a passive science. Here is Victor J. Katz in A History of Mathematics, second edition, page 196:

"The Chinese emperors, like rulers elsewhere, had always been interested in problems of the calendar, that is, in predicting various celestial events such as eclipses. Unfortunately, Chinese astronomers were not very successful in predicting eclipses because they did not fully understand the motions of the sun and moon. Indian astronomers, because of Greek influence in the creation of a geometrical model, were more successful. Thus in the eighth century, when Buddhism was strong in both India and China and there were many reciprocal visits of Buddhist monks, the Chinese emperors of the Tang dynasty brought in Indian scholars as well to provide a new expertise….In 724, the State Astronomical Bureau of the Tang dynasty began an extensive program of field research…These observations were then analyzed by the chief astronomer, Yi Xing (683-727), himself a Buddhist monk. Yi Xing's goals was to use these and other observations, as well as various interpolation techniques, to calculate the length of such shadows, the duration of daylight and night, and the occurrence of eclipses, whatever the position of the observer. (Yi Xing was not aware of the sphericity of the earth and therefore could not make use of the classic Greek model.)"

I have consulted a number of balanced, scholarly works, and even a rather pro-Chinese book such as A Cultural History of Modern Science in China by Benjamin A. Elman admits that Chinese scholars still believed in a flat Earth in the seventeenth century AD, when European Jesuits missionaries introduced new mathematical and geographical knowledge to China:

"For instance, the first translated edition of Matteo Ricci's map of the world (mappa mundi), which was produced with the help of Chinese converts, was printed in 1584. A flattened sphere projection with parallel latitudes and curving longitudes, Ricci's world map went through eight editions between 1584 and 1608. The third edition was entitled the Complete Map of the Myriad Countries on the Earth and printed in 1602 with the help of Li Zhizao. The map showed the Chinese for the first time the exact location of Europe. In addition, Ricci's maps contained technical lessons for Chinese geographers: (1) how cartographers could localize places by means of circles of latitude and longitude; (2) many geographical terms and names, including Chinese terms for Europe, Asia, America, and Africa (which were Ricci's invention); (3) the most recent discoveries by European explorers; (4) the existence of five terrestrial continents surrounded by large oceans; (5) the sphericity of the earth; and (6) five geographical zones and their location from north to south on the earth, that is, the Arctic and Antarctic circles, and the temperate, tropical, and subtropical zones."

Japan received much scientific and technological information from China and with Korean immigrants during the sixth, seventh and eighth centuries AD. Until contact with Europeans, Japanese astronomy was based almost entirely on that of the Koreans and the Chinese. They borrowed institutional patterns from China, but these did not fit Japan equally well and the knowledge of astronomy and calendar-making became increasingly hereditary, which depressed scientific standards. They also took over some of China's flaws, for instance with ranking astrology and divination higher in the scale of human wisdom than calendar-making and what we would consider serious mathematical astronomy.

The Chinese mathematical tradition was significant (certainly better than the non-existent Roman one), but less influential than the Indian one. I would be tempted to say that China was a hardware civilization whereas India was a software civilization. The truth is that given the size of their economy and population, the Chinese were weaker in mathematics than might have been expected if you believe in an economic explanation for scientific advances. The Japanese and Korean mathematical traditions were again largely dependent upon the Chinese one. Given the level of technological sophistication these nations have shown and the talent they have demonstrated in using mathematics, they have contributed surprisingly little to developing mathematics, whereas the European contribution to global mathematics is greatly disproportionate. This proves that although some minimum level of wealth is a necessary cause for the growth of science (extremely poor people concentrate on surviving, not on inventing calculus or comparative linguistics), it is by no means a sufficient one.

From the fourteenth until the twentieth century, almost all important global advances in mathematics were European. I would be tempted to say that European leadership was stronger in mathematics than in almost any other scholarly discipline. Perhaps the simplest explanation for why the Scientific Revolution happened in Europe is because the book of nature is written in the language of mathematics, as Galileo once famously stated, and Europeans did more than any other civilization to develop or discover the vocabulary of this language.

The introduction of the telescope was a major watershed in the history of astronomy, but we should remember that it alone did not create modern astronomy. The birth of astrophysics in the late nineteenth century came through the combination of the telescope with photography and spectroscopy, all inventions that were exclusively made in Europe. Spectroscopy could not be developed until chemistry as a scientific discipline had been formed, which only happened in Europe. New fuels, engines and materials later made space travel possible. Asian rockets were powered by gunpowder and weighed a couple of kilograms at most. They could not have challenged the Earth's gravity and explored the Solar System. The Saturn V rocket that launched Apollo 11 on its journey to the Moon in 1969 used liquid hydrogen and oxygen, elements which had been discovered in Europe. The very concept of gravity, too, was developed only in Europe. The exploration of the Solar System and the universe at large was to an overwhelming degree made possible by a single civilization alone, the Western one.