Despite evidence for the ‘other humanity’ in the East, a civilization that went down the inductive path, ship after ship of enthusiastic but ignorant Western scholars set their sails for Asia, their eyes fixed on analyzing and deconstructing the hype and propaganda of ‘the exotic Other’ and proving that the East is a mere repressed, introverted Sleeping Beauty, denying the existence of the East-West dichotomy, ignoring all warnings, only to discover the same old truth over and over again: The East constitutes an entirely different type of humanity. It is holistic, non-analytical, and spiritual – it is integration-based, and it is very capable and strong. We come back to that in a minute. But first some more facts:
Most sinologists and universal historians today more or less agree that before Xu Guangqi (徐光启, 1562-1633) published his translation of the first six books of Euclid’s Elements of Geometry in 1607, this kind of Greek/Hellenistic, analytic-deductive driven mathematics and axiomatic proof-findings had been systematically unknown to Asia (Needham, 1964; Hart, 1999; Spence, 2001). Indeed, it took China’s mathematicians roughly 250 years, until in 1851 Alexander Wylie (1815-1887) and Li Shanlan (李善兰, 1811-1882) published the second half of the translation of Euclid’s Elements of Geometry, to realize the practicability of axioms at all (Horng & Wann-Sheng, 2001).
What started off as cooperation between Xu Guangqi and Matteo Ricci in 1607 later became the nucleus of an entirely new branch of Western scholarship – ‘The History of Science in China.’ Why is that such an interesting new branch of scholarship? Well, since it was European missionaries who proactively entered China and taught the Chinese, not some Chinese missions to Europe, and since the Western missionaries were believed to possess the religion of truth and analytical sciences, how was it possible that an atheistic, non-analytical civilization like China nevertheless had developed into an intelligent, fully-functional society that in countless fields like art, agriculture, astronomy, economics, logistics, medicine, and mechanics was more advanced than its European counterparts? That is why the ‘History of Science in China’ had to be carefully reconstructed in the West in order to make sense of it all; the only problem was that Western scholars translated almost all of China’s socio-cultural originality – its concepts and non-European ideas – into convenient European taxonomies (a fascinating topic and text-book case of cultural imperialism which unfortunately we cannot discuss in detail here).
The Jesuits in China, as I said elsewhere before, were mostly successful simply because they did not insist on forcing the whole of Eurocentric catechism on the ordinary Chinaman; on the contrary, they even adapted to Confucian scholarship. However, what they reported back to Europe about the kind, good-hearted, intelligent, and confident Chinaman and his unique state morality and Confucian/Daoism/Buddhism mode of conduct often nurtured a certain dislike for the ‘second humanity.’ In comparison to Muhammad’s teachings in the Quran, which is after all a relatively young religious canon (c. 600), Islam is essentially dogmatic but practical, thus having turned into a physical competitor, whereas the much older I Ching (易经, c. 1050 BC-256 BC), Dao De Jing (道德经, c. 600 BC), the Buddhist sutras (佛经, c. 500 BC), or The Analects (论语, ca. 479 BC-221 BC) seem to cover deeply philosophical issues, metaphysics, difficult mathematics, and a complex moral system, much of it posing some serious challenges to some of those ambivalent wisdoms offered in the Bible. In other words, Christianity had found some sort of enlightened competitor.
The German philosopher Friedrich Schelling (1775-1854) was convinced that already in prehistoric times, China became unique, ‘the other humanity,’ distinct from the rest of the world, and, furthermore, that is was the only living remnant of a time before the world was divided into two different humanities (Schelling, 1842). He also branded China “un univers sans Dieu.” Johann Gottfried Herder (1744-1803) labeled it “an embalmed mummy wound in silk” and the Chinese “corner people.” Finally, Alain Peyrefitte (1925-1999), author of The Collision of Two Civilizations, famously called it “l’empire immobile” (Bernie, 2005) because of its compliance and, ultimately, meekness.
Same Europeans who believed in God and the scientific ways, sensing a lack both of religion and science in China, assumed there had been no scientific advancement in China before the Europeans arrived. Not quite a fair observation, as we know today. It is true that before the introduction of Western sciences, there had been indeed no need for foreign axioms. But that was simply because East Asia had cultivated its own practical brand of mathematics, primarily relying on induction and analogical reasoning. In fact, this stubborn and very different ‘scientific’ approach of the Chinese has infuriated the European Imperialists ever since, culminating in the famous, almost hysterical saying by Sir Reverant Arthur Smith in The Chinese Characteristics (1890) that “the Chinese mind absolutely must be algebraic, while the Western mind is arithmetical” (Smith, 1890).
The Chinese Characteristics, mainly because of its style, is probably the single most outrageous book on the peculiarities of the Chinaman ever written, causing waves of anti-Western resentment among the Chinese leading up to the Boxer Rebellion against the Western imperialists at the turn of the nineteenth century (1899-1901). Yet, Smith simply recounted what every scientist in the field already knew: There is the integration-based East, and there is the analysis-based West, and no third mode of reasoning other than that of the inductive and deductive modes has ever been achieved by human beings. It seemed incredible, but here was Asia, which excelled more in the inductive ways, and there was Europe, which excelled more in the deductive ways. And that was it.
Gems of ancient Chinese inductive-driven mathematics are: The Book of Changes [易经], written during the Zhou Dynasty (1050 BC-256 BC, possibly originated around 2800 BC by Fu Xi [伏羲]); the Book of Poetry [诗经] with pieces written around the year 1000 BC; the Mo Jing [墨经] (470 BC-390 BC); The Nine Chapters on the Mathematical Art [九章算术] (c. 200 BC-AD 179). Here I should add that The Nine Chapters had a great influence on the Japanese scholar Seki Takakazu who developed – during the Edo Period (1603-1867) – another arithmetical, idiosyncratic mathematics called ‘wasan’ (和算). Other valuable works on Chinese mathematics include the Zhoubi Manual [周髀算经] written during the Han period (c. 202 BC-AD 220); the Sea Island Manual [海岛算经] written during the Three Kingdoms period in the year 263; and the Jade Mirror of the Four Unknowns [四元玉监] written in 1303. Zhu Shijie [朱世杰] (1303) once said, in the tradition of The Book of Changes: “‘One’ is the source of all mathematics” and that those words of the Dao De Jing (道德经, c. 600 BC): “The Dao begets the One; the One begets the Two opposites” really summarize (Chinese) mathematics: “All stems from the number ‘one.’” By this, Zhu Shijie perfectly harmonized Chinese mathematics with the Eastern concept of ‘oneness,’ thus once more effectively defining the essence and story of most Eastern ‘philosophies’ – be it the teachings of Siddhartha Buddha (563 BC-483 BC), Vyasa of the Mahabharata (c. 800 BC), or the Four Confucian Classics (四書五經, before 221 BC).
Someone who is genuinely interested in mathematics may as well call the cited works above the “Chinese Computation Classics.” Xu Guangqi made some genuine attempts to integrate Western and Chinese mathematics, but ended up being all too pragmatic about it – if a Chinese equation led to the same result as Western mathematics did, it was there to stay, if not, it was to be abandoned (Engelfriet & Siu, 2001).
Chinese mathematics, which had a great influence on mathematics in Korea and Japan as well, flourished until approximately the twelfth and thirteenth centuries, fell into decline after the arrival of the Jesuits and Westerners and their teachings about arithmetical mathematics and science, and became almost forgotten during the nineteenth and twentieth centuries (Jami et al., 2001; Engelfriet & Siu, 2001). But that does not necessarily mean that it was all ‘no good’ – on the contrary:
Zhu Shijie, in his Jade Mirror, for example, teaches a diagram similar to that in Blaise Pascal’s Traité du triangle arithmétique, the latter of which was not published until 1665 in Europe. Why had the world waited 362 years for Pascal’s triangle when Zhu Shijie’s diagram could have initiated the same mathematical revolution? A convincing answer to that is given in the Study of the Fourteenth-Century Manual on Polynomial Equations by John Hoe:
Chinese written language enabled Chinese mathematicians to express themselves with a conciseness that is almost impossible to attain in highly-inflected natural languages, using an alphabet, such as prevailed in Europe. Thus, Chinese were able to deal with problems which in the West could not be tackled until a suitable mathematical symbolism had been developed. At the same time, this meant that the Chinese mathematicians never had the incentive to develop a fully symbolic algebraic notation, since the need for one was never as acutely felt as in Europe. (John Hoe, 2007)
Language barriers, cultural prejudices, ignorance, or pure spite? Most likely, these were all factors, among others. In this regard, not a lot has changed in the last 400 years. Don’t expect many American or European citizens, even the more educated ones, to master their host country’s language or to know anything about their host country other than the information they have obtained from English-language sources and textbooks. It is not going to happen; it is wishful thinking. As the German-Swiss writer Hermann Hesse once wrote: “We cannot and we must not become Chinese, and at heart we don’t want to either. We must not seek ideal or higher meaning of life in China or in any other thing of the past; otherwise we lose ourselves and adhere to a fetish” (Hesse, 1921).
Already in 1627, Xu Guangqi [徐光启] applied scientific methods and conducted experiments – as demonstrated in the vast corpus of his works leading to his Almanac of Agriculture (农政全书, 1627) – on crops, sweet potatoes, and water irrigation, to name but a few (Jami, 2001). The results were impressive. In 1630, China could feed its 70 million people. Some 120 years later, when Great Britain was forced to think scientifically about how to improve her agriculture in order to feed her ‘overpopulation’ of some 5.7 million, China was already feeding a nation of roughly 200 million.
Similarly, the Chinese Traditional Calendar by Guo Shoujing (郭守敬, 1231-1316), which is based on the synodic month, or time taken by the moon to make a complete circle around the Earth, had been invented at least 300 years before the Gregorian calendar, which is in effect a solar calendar, in Europe (Hashimoto, 2001).
Talking more about sciences, Liu Hui [刘徽] in his Sea Island Manual (海岛算经, c. 263) measured the sun’s height by the lengths of a shadow cast on an upright rod. By comparing geographical distances and spaces, the Chinese employed their own mechanical, scientific methods that relied on empirical proofs devised by their ancestors, rather than axiomatic proofs preferred by the ancient Greeks and devised by their ancestors (Jami, 2001). As a rule, in traditional Chinese mathematics, a geometric problem was almost universally converted into an algebraic problem, quite different from the geometrical approach used in Euclid’s Elements.
Surprisingly, today traditional Chinese mathematics like mechanical proofs or ‘Wu Wenjun’s method’ are experiencing a revival in computational sciences, just as Chinese medicine, Chinese education, and Chinese politics are in their respective fields; all these disciplines are now striving again for recognition in world science.
To sum up, only after the West, culturally and scientifically, invaded the Eastern hemisphere, did mathematics in China become the universally axiomatic-deductive driven vehicle it is today. But Western invasion was not the precursor for sciences in China. Science had been in East Asia before, if only in a different, unique fashion (Needham, 1956; Jami, 2001).
Fortunately, in this century, the Western-fabricated fairy tale of former Eastern ‘backwardness’ and Western ‘glory’ has been dispelled. In reality, Eastern knowledge and Western knowledge are fairly balanced and complementary, and always have been.
As Francis Bacon and James Clerk Maxwell (1831-1879, mathematician and theoretical physicist) have sufficiently explained, ideally, the most sincere science is done today when both the inductive and the deductive methods find their due application. In some disciplines we prefer the inductive way, namely in the arts, while in many disciplines we tend to use both, like in sociology, archaeology, psychology, philosophy – the humanities. In others still we prefer the deductive way, like in mathematics, physics, biology, chemistry – the classical sciences. Yet ideally, induction and deduction should be used in a more balanced way.
Maxwell’s equations are a good example of a successful synthesis: He carefully applied first the deductive method in proving several equations in seemingly separate fields of research, then the inductive method to demonstrate that electricity, magnetism, and even light are all manifestations of the same phenomenon: the electromagnetic field. It is like seeing each tree, and then the whole forest, but never both quite at the same time. This demonstrates an ‘ideal’ way of problem-solving by picking up a single successful case out of a million yet undecided ones.
A discovery of revolutionary proportions in the evolution of culture: An entire civilization, the East, goes down a more induction-based path, arriving at universals; while another civilization, the West, goes down the exact opposite, a more deduction-based path, arriving at particulars? If that is indeed what happened, it would constitute a discovery of great consequence: It would mean that ‘superior’ Western history has been ideologically and methodically biased, if not inherently flawed, throughout the ages:
The academic discipline of history is inevitably ideological in essence. Regardless of what might be the case with individual historical events, historical narration is always the result of a series of selective choices, so that the influence of the historian’s standpoint is inescapable. (Toshio Kuroda, 1990)
Universal history, as explained in this book, requires at least two points of view. As Joseph Needham (1951), Sir Geoffrey Ernest Richard Lloyd (1996), and Jonathan Spence (2001) – all three were married to Chinese women – demonstrated to Western audiences, China’s contributions to humankind in traditional mathematics, medicine, statecraft, and agriculture had developed even before the First Qin Emperor’s unification of China up to the Song (宋 960-1127-1279) and Yuan Dynasties (元 1271-1368) (Wu, 2007). In the course of just over one publication series, Science and Civilization in China (1954-2000), European scholars were up in arms at the sensational, if not horrifying news that Europeans owe their paper money, matches, umbrellas, playing cards, and whisky all to some blueprints of an unfamiliar Chinese mastermind (Temple, 2007). It comes as no surprise that the Chinese Communist Party and Chinese Ministry of Education readily adopted Needham’s thesis that so more often than not eulogizes those good old days When Asia Was the World (Gordon, 2007).
In addition, and to the embarrassment of serious scholars, the ‘History of Sciences in China’ became the hobbyhorse for tens of thousands of amateur scholars, exchange students, tourists, and backpackers from around the world who tried to trace anything European or American back to its alleged Asian roots. Today, newspapers, computers, soccer, even German sauerkraut and sausages, Italian pasta and pizza, Reggae and Bob Marley have their firmly established Chinese progenitors (among the latter of whom are Vincent and Patricia Chin of Randy’s Records in Jamaica, if you insist on knowing).
Yet, whatever this new wave of twenty-first century ‘Eastern enlightenment of the West,’ often mixed with institutionalized overstatement and euphemism in sensation-seeking media or some individuals’ fancies – even the most frivolous ambition to remedy the past failures of Asia for the glory of her future cannot hide the fact, as the historians Joseph Needham, Catherine Jami, Peter Engelfriet, Geoffrey Lloyd, and Li Tiangang described it, that China in particular had not developed or not sufficiently developed anything in the way of science and technology that could compete with the Western Imperialist’s model, which in turn attested the Chinese were a people of ‘arrested development’ (Gu, 1922). I call the Western Imperialist’s model “rather lucky than good,” because some scholars, by bending history to the point of breaking, want us to believe that ‘evil’ Western dominance in Asia can only be explained by the lucky insensitivity of scientific discoveries like rifles and cannons (Chirot, 1991), surpassing the firecrackers made of China’s gunpowder. Others, like Janet Abu-Lughod (1989) for example, point to the ‘moment of China’s political weakness’ during the fall of the Mongols in the thirteenth century and coined the phrase ‘bad luck for Asia,’ which was “exploited by the Europeans who lacked any singularly innovative entrepreneurial scientific, or otherwise worthwhile advantages, except perhaps an exceptionally nasty tendency to conduct their large-scale trade as piracy” (Abu-Lughod, 1989).
Despite Western dominance, the Chinese ‘civilization’ (the correct name is wenming [文明]) had its advantages. The strong Confucian tradition of self-cultivation, learning, and memorization, with the translation and integration of foreign thoughts “for the purpose of understanding the West on Chinese terms” (Malhotra, 2011) reaching back to the early Buddhist monks during the Six Dynasties (222-589), has a remarkable consistency that ultimately proves a point:
It is important you should remember, that this nation of children, who live a life of the heart, […] have yet the power of mind and rationality […] which has enabled them to deal with the complex and difficult problems of social life, government and civilization with a success which, I will venture to say here, the ancient and modern nations of Europe have not been able to attain. (Gu Hongming, 1922)
I could go on, but before I do: It might strike some Europeans as outright offensive, but the truth is that they are not the only ones claiming the title of the fittest when it comes to ‘surviving’ history. To put it into historical perspective: The Chinese Empire was united in the year 221 BC under the Qin (秦) Emperor, some 1,997 years before Thomas Jefferson drafted the Declaration of Independence for the USA in 1776. India’s sense of unity, ethnic diversity and, yes, democratic roots grew out of necessity because of her ‘composite religious culture’ some 2,500 years ago. By contrast, the Europeans today are struggling even with a constitutional treaty.
Two Successful Models
Pattberg, Thorsten (2013), The East-West Dichotomy, Foreign Language Press, Beijing