Chapter 8 – Two Successful Models
Despite the evidences of the “other humanity”, 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 set 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 all over again: The East constitutes an entirely different type of humanity: it is holistic, non-analytic 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 with the co-operation of Xu Guangqi and Matteo Ricci in 1607 later became the nucleus of an entirely new branch of Western scholarship – ‘The History of Science inChina’. Why is that such an interesting new branch of scholarship? Well, since it was European missionaries who pro-actively 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 atheist, non-analytical civilization like China nevertheless had developed into an intelligent, fully-functional society that in countless fields like art, agriculture, astronomy, economics, logistic, medicine and mechanics was more advanced than its European counterparts. That is why the ‘History of Science inChina’ had to be carefully reconstructed in the West in order to make sense of it all.
The Jesuits in China, as I said elsewhere before, were mostly successful simply because they did not insist on implementing the whole of euro-centric 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 Mohammad’s teachings in the Quran – which is after all a relatively young religious canon (c. 600 AD) -, Islam is essentially dogmatic but practical orientated, thus having turned into a physical competitor, whereas the much older I Ching (易经, c. 1050-256 BC), Dao De Jing (道德经, c. 600 BC), the Buddhist sutras (佛经, c. 500 BC), or The Analects (论语, ca. 479-221 BC) seem to cover deeply philosophical issues, metaphysics, difficult mathematics and a complex moral system, much of it that puts some serious challenges to some of those ambivalent wisdoms offered in the Bible. In other words, Christianity had found some sort of enlighten competitor:
The German philosopher Friedrich Schelling (1775-1854) was convinced that already in prehistoric times China became her own or 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” or “corner people”, and, finally, Alain Peyrefitte (1925-19999), author of The Collision of two civilizations, famously called it: “l’empire immobile” (Bernie, 2005), because of its compliance and, ultimately, meekness.
Same faithful Europeans who believed in God and the scientific ways, and – sensing a lack both of religion and science in China – assumed there had been no scientific advancement in China before the European arrival. 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 driven mathematics, primarily relying on induction and analogical reasoning. In fact, this stubborn and very different “scientific” approach of the Chinese infuriated the European Imperialist ever since, culminating in the famous, almost hysterical saying by Sir Rev. Arthur Smith in his The Chinese Characteristics (1890), that “the Chinese mind absolutely must be algebraic, while the Western mind is arithmetical” (Smith, 1890).
Chinese Characteristics, mainly because of its style, is probably the single most outrageous book on the peculiarities of the Chinaman ever written, causing rushes of anti-Western resentment among the Chinese leading up to the Boxer Rebellion against the Western imperialists in 1899-1901. Yet, Smith simple 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, while there wasEurope which excelled more at 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 (1050-256 BC, while possibly originated around 2800 BC by Fu Xi [伏羲]), the Book of Poetry [诗经] with pieces written around 1000 BC, the Mo Jing [墨经] (470-390 BC), The Nine Chapters on the Mathematical Art [九章算术] (c. 200 BC-179 AD) [the Nine Chapters had a great influence on the Japanese scholar Seki Takakazu who developed – during the Edo Period in 1603-1867 – another arithmetical, idiosyncratic mathematics called ‘wasan’ (和算)], the Zhoubi Manual [周髀算经] written during the Han period (c. 202 BC to 220 AD), the Sea Island Manual [海岛算经] written during the Three Kingdoms period in 263 AD, and the Jade Mirrow of the Four Unknows [四元玉监] written in 1303 AD. Zhu Shijie [朱世杰] (1303 AD), in the tradition of the I Ching (易经, c. 1050-256 BC): “’One’ is the source of all mathematics”, and Dao De Jing (道德经, c. 600 BC): “The Tao begets the One; the One begets the Two opposites”, summarizes (Chinese) mathematics: “All stems from the number ‘one’”. By this Zhu Shijie perfectly harmonizes Chinese mathematics with the Eastern concept of ‘oneness’, thus once more effectively summarizing the essence of most Eastern philosophy – be it the teachings of Siddhartha Buddha (563-483 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 very 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 abandon (Engelfriet & Siu, 2001).
Chinese mathematics, which had a great influence on mathematics in Korea and Japan as well, flourished until approximately the 12th and 13th century, fell into decline after the arrival of the Jesuits and Western and their teachings about arithmetical mathematics and analytic-based science, and became almost forgotten during the 19th and 20th century (Jami et. al, 2001, Engelfriet & Siu, 2001). But that does not necessarily mean that it was all ‘no good’ – on the contrary:
Zhu Shiejie [朱世杰], in his Jade Mirrow of 1303, for example teaches a diagram similar to that in 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 done the same trick? A convincing answer to that is given in the Study of the Fourteenth-Century Manual on Polynomial Equations by J. 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 inEurope. 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 inEurope. (J. Hoe, 2007)
Language barriers, cultural prejudices, ignorance or pure spite? One is dread to think it’s all of it, and a lot more than that, and that is hasn’t changed much during the last 400 years. Don’t expect any great proportions of American or British citizens, even the more educated ones, ever to learn the host’s language or to know anything about the host other than the information they got from English textbooks. It is not going to happen, it is wishful thinking.
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, whenBritain was forced to think scientifically about how to improve its agriculture in order to feed its “overpopulation” of some 5,7 million,China already nurtured a nation of roughly 200 million.
Similar far ahead of its time, the Chinese Traditional Calendar by Guo Shoujing (郭守敬 1231-1316) which is based on the synodic month (time taken by the moon to make a complete circle around the earth) on which later the agrarian Twenty-Four Fortnightly Periods (节气 Jie Qi) were based, 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 AD) measured the sun’s height by the lengths of a shadow cast on an upright rod. By comparing geographical distances and spaces, the Chinese scholars 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 lets say in Euclid’s Elements.
Surprisingly, today traditional Chinese mathematics like mechanical proofs or ‘Wu Wenjun’s method’ experience a revival in Computational Sciences, just as Chinese medicine, Chinese education and Chinese politics do in the other 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 inChinabecome the universally axiomatic-deductive driven vehicle it is today. But Western invasion was not the precursor for sciences inChina. Science had been inAsiabefore, if only in a different fashion and unique manner (Needham, 1956; Jami, 2001).
Fortunately, the Western fabricated fairy-tale of former Eastern ‘backwardness’ and Western ‘glory’ in this century now lies tattered and wrenched. In reality, Eastern and Western knowledge is fairly balanced and complementary, and always has 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 – the arts; in many we tend to sway from side to side, like in sociology, archeology, psychology, philosophy – the humanities; in others we prefer the deductive way, like in mathematics, physics, biology, chemistry – the classical sciences, but ideally, induction and deduction should be used more balanced.
Maxwell’s equations are a good example of a successful synthesis: he carefully applied first the deductive methods in proving several equations in seemingly separated 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 lesson, unfortunately, describes an ‘ideal’ solution 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 what indeed happened, it would constitute a discovery of great consequences; it would mean that Western superior 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 all over this book, has at least two angles of view. As Needham (1951), G. E. R. Loyd (1996), J. Spence (2001) (all three were married to Chinese women, if you must know) demonstrated to Western audiences, China’s contributions to humankind in traditional mathematics, medicine, statecraft, and agriculture developed since quite remote times before the First Emperor Qin’s unification of China up to the Song (宋 960-1127-1279) and Yuan Dynasty (元 1271-1368) (Wu, 2007). In the course of just over one publication series Science and Civilization in China (1954-2000), European scholarship was to cry out loud at the sensational, if not horrifying news that Europeans own their paper money, matches, umbrellas, playing cards and whisky all to some blueprints of an unfamiliar Chinese mastermind (Temple, 2007). Unsurprisingly, the Chinese Communist Party, Chinese Ministry of Education, readily adopted Needham’s thesis that so more often than not applauds, eulogizes and praises those good old days When Asia was the World (Gordon, 2007), a superstition that rarely makes sense today to anyone except some Western sinologist and orientalists.
In addition, and to the embarrassment of serious scholarship, 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, taking up anything European or American and tracing it back to some Asian roots of origin. Today, newspapers, computers, soccer, even German sauerkraut and sausages, Italian pasta and pizza, Reggae and Bob Marley have their firmly established Chinese progenitors (the latter of whom there are Vincent and Patricia Chin of Randy’s Records inJamaica, if you insist on knowing).
Yet, whatever this new wave of 21st century ‘Eastern enlightenment to the West’, often mixed with institutionalized overstatement and euphemism in sensation-seeking media or some individuals’ fancies may bring, even the most frivolous ambition to remedy the past failures of the Asian for the glory of her future cannot cover the fact, as Needham, Jami, Engelfriet, Lloyd, and Li 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 – rather lucky than good – Western Imperialist’s model, which in turn attested the Chinese being a people of ‘arrested development’(Gu, 1922). I said “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 insensitive of scientific discoveries like rifles and cannons (Chirot, 1991) surpassing the firecrackers made of China’s gunpowder. Others, like Jant Aby-Lughod (1989) for example, point to the ‘moment of China’s political weakness’ during the fall of the Mongols in the 13th 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” (Aby-Lughod, 1989).
Nevertheless and despite Western dominance, the Chinese civilization had its advantages. Its strong tradition of learning, memorization, with translation and integration of foreign thoughts reaching back to the early Buddhist monks during the Six Dynasties (222-589 AD), there is 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 rather propose this midway conclusion. It might strike some Europeans as outright offensive, but the truth is that they are not alone claiming the title of the fittest in ‘surviving’ history. To put it into historical perspective: the Chinese Empire was united in 221 BC under the Qin Emperor (秦), some 1,997 years before Jefferson drafted the Declaration of Independence in 1776 AD. India’s sense of unity, ethnic diversity and, yes, democratic roots too grew out of necessity because of its ‘composite religious culture’ some 2500 years ago. The Europeans, till to this date, struggle even with a constitutional treaty.