Event category: Premodern History & Archaeology

The Global and the Local under the Tang
Wednesday
2:00 pm – 3:45 pm
Room B

• Michael Höckelmann, “Civilising Mission: Local and Global as Colonial Spaces in Tang Visions of Empire”
• Kelsey Granger, “Intercultural Marriage in Tang China: An Intersection between ‘Global’ and ‘Local’ Concerns”
• Chen Xue, “Foreigners or Natives? The Diverse Interpretations of the Identity of ‘Shatuo Turks’ from the Late Ninth to the Eleventh Century”
• Lance Pursey, “’A Sea of Rhymes, a Mirror of Sources’: The Eclectic Literary Scene in Huzhou in the Dali Era (766–779) as a Test of High-Mid Tang ‘Glocalisation’”

Scholars have labelled the Tang 唐 (618–907) ‘China’s Cosmopolitan Empire’ (Lewis 2009). Tang elites were exceptionally open to global influences in arts, music, and religion, while a great number of foreigners served in its civil and military services. Aside from the foreign, the local played a huge role in Tang society, too: While cultural and political life centred on the capitals Chang’an 長安 and Luoyang 洛陽 in the north, the population began shifting to the south and thus prepared the economic revolution of the eleventh through thirteenth centuries. During much of the first half of the dynasty, the court was perambulating between Chang’an and Luoyang every year, and most members of the official service spent considerable parts if not all of their careers in one of the countless prefectures and counties of the realm. While the court from the mid-eighth century onwards remained entrenched in Chang’an—the occasional flight from rebels or invaders aside—many literati turned to the surrogate courts of provincial commissioners in the hope for better career prospects. At the same time, foreign invaders and traders remained a constant presence in most regions of the empire. What impact did the ‘global’ and the ‘local’ have on the social, cultural, and political life of the Tang? Is it appropriate to consider the Tang part of a ‘Global Middle Ages’ (Holmes and Standen 2018), emphasising its interconnectedness with the wider world, or is it necessary to employ other concepts in the analysis of this interplay?

Michael Höckelmann, “Civilising Mission: Local and Global as Colonial Spaces in Tang Visions of Empire“

Despite Tang China’s (618–907) alleged cosmopolitanism, contemporary writings such as frontier poems (biansai shi 邊塞詩) depict the local and the global as dismal places, where an official only ended up as a punishment. Areas like the South (Lingnan 嶺南), the Protectorate to Pacify the West (Anxi duhufu 安西都護府), and the many bridle-and-halter prefectures (jimi zhou 羈縻州) scattered throughout the realm all served as frontiers or counterpoints to the civilised centres of the court and capital(s). The ‘locals’ were the stereotypical other, uncouth, raw, even barbarian, upon which the magistrate, prefect or commissioner (and his aides), who came from the centre, exerted a civilising influence much like colonial officials. The interplay of global and local is evident in the chapters on prefectures (zhoujun 州郡) and borderlands (bianfang 邊防) that appear back to back in Du You’s 杜佑 (734–812) Tongdian 通典. Geographic treatises such as Li Jifu’s 李吉甫 (758–814) Yuanhe junxian tuzhi 元和郡縣圖志 were a way of gaining textual control over a hinterland of which large swaths were still undiscovered country. This paper looks at contemporary writings on local and border administration such as those above, institutional histories, and inscriptions (e.g., ting biji 廳壁記), to highlight the interplay between local and global as frontier zones or colonial spaces in the framing of bureaucracy and empire in the Tang period.

Kelsey Granger, “Intercultural Marriage in Tang China: An Intersection between ‘Global’ and ‘Local’ Concerns“

Research on Tang China is often rooted in considering global and/or local concerns within areas of daily life. Being a period noted both for its early cosmopolitanism and its later xenophobia as well as the complex interplay between identity, ethnicity, and cultural norms on a global and local scale, it is surprising that little attention has been paid to intercultural marriage within this framework. Much scholarship assumes that legal restrictions set out in Tang lüshu yi 唐律疏議 were fully implemented and followed in daily life, whereas my research seeks to prove that there were differences between state and popular perceptions of intercultural marriages as can be seen when comparing several extant xiaoshuo 小說 with accounts from the official histories. Equally, it can be tempting to assume that, amongst the increasingly intolerant legislation and outlook of the late Tang period, that intercultural marriages were heavily discouraged. Again, my research seeks to prove that these marriages often inhabited ‘grey areas’ of cross-cultural interactions, with accounts of such unions continuing to be written throughout the Tang period albeit producing differing reactions in authors and historians. Finally, each account studied herein is shaped not only by its author and its textual history but also by the geopolitical local atmosphere at its conception. By means of contextualising each case-study, I, therefore, hope to bring nuances therein to light and expand on the global and local anxieties, agendas, and agency at play within these accounts.

Chen Xue, “Foreigners or Natives? The Diverse Interpretations of the Identity of ‘Shatuo Turks’ from the Late Ninth to the Eleventh Century“

This paper questions the ethnic binary between Shatuo Turks and Chinese of the Five Dynasties’ ruling families. In modern historiography, Later Tang, Later Jin and Later Han were normally depicted being of Turkic origin, and historians tend to believe that this supposed ethnic difference determined historical figures’ choices and behaviours at the time. Many key events, such as the fictive kinships between Liao emperors and the so-called Shatuo monarchs, Shi Jingtang’s cession of the Sixteen Prefectures to Liao, and Later Zhou and Song’s determination to reclaim these territories, have constantly been explained via their ethnic differences. By examining sources especially tomb epitaphs and historical writings of late Tang, the Five Dynasties, Liao, and Northern Song, this paper argues that the educated elites at the time, including the so-called Shatuo imperial families of the tenth century, in fact had no consensus on who bore the Shatuo Turkic identity. Rather, the ‘Shatuo Turkic’ emperors and their forebears appeared in their contemporary discourses as having diverse geographical, cultural, or ethnic origins. Their ‘barbarian’ identity was more a later Song construction than a historical reality. The paper emphasises that ethnicity was only one of many discourses that shaped the ninth- to eleventh-century figures’ ideologies and behaviours, underscoring the fluidity of identities at the time which the Turkic–Chinese dichotomy fails to account for.

Lance Pursey, “’A Sea of Rhymes, a Mirror of Sources’: The Eclectic Literary Scene in Huzhou in the Dali Era (766–779) as a Test of High-Mid Tang ‘Glocalisation’”

The vision of cosmopolitan, even globalised, Tang empire disproportionately focuses on its capitals and its north and western frontier relations, whereas much of the southeast of China is neglected.
This paper examines five literary figures who crossed paths in the Jiangnan city of Huzhou in the Dali era to show that educated members of society were productive and influential outside the capitals and outside of officialdom. By examining the geographical places and textual allusions in the lives and works of the official Yan Zhenqing, the “tea saint” Lu Yu, the critic and poet Buddhist monk Jiaoran, the Daoist nun poet Li Ye, and the reclusive painter Zhang Zhihe I will reveal a cultural sensibility that was not directed towards the court and capitals, nor to a ‘globalised’ world beyond.
Rather, Jiangnan was becoming a revived cultural centre to rival the capitals of Chang’an and Luoyang, a centre that drew not on political prominence and cosmopolitanism but on eclectic traditions and innovation. And connected to other areas in the empire outside of the capitals.
If not everywhere in the Tang is cosmopolitan does it earn the title cosmopolitan empire? I argue that the Tang was an eclectic empire whose literati in different regional and official spheres drew in different degrees upon rich cultural heritages from both home and abroad. This eclecticism manifests in their literary output which resembles the title of Yan Zhenqing’s lost leishu, “A sea of rhymes, a mirror of sources”.

Encounters
Wednesday
9:00 am – 10:45 am

• Chaired by Christine Moll-Murata
• Sebestyén Hompot, “Zheng He’s Missions: A Critical Discourse Analysis of Current Mainland Chinese Historiography”
• Xiaobai Hu, “Exploring the Foreign Land: The Founder of Ming China and His Tibet Experiments”
• Leiyun Ni, “Provision as a Negotiation Site: Sino-Anglo Encounters in Canton”

Sebestyén Hompot, “Zheng He’s Missions: A Critical Discourse Analysis of Current Mainland Chinese Historiography”

The present paper investigates the mainland Chinese academic discourse of the last 20 years on the Zheng He missions (1405–1433) of the early Ming period. The theory and methodology of the relevant research project is based on Critical Discourse Analysis (CDA), most notably the approach of the Duisburg School (Margret Jäger, Siegfried Jäger, et al.) and the Discourse-Historical Approach of Ruth Wodak et al., with further insights gained from scholarship on CDA in the Chinese context. The research project involves quantitative analysis relying on digital tools (publication statistics, citation networks, word frequencies), CDA-based qualitative analysis of a selected number of relevant academic works, as well as expert interviews as part of a research stay in China (March–April 2020). The research project is intended to explore the recent trends in mainland Chinese research on the Zheng He missions, the underlying global and domestic power relations and ideologies, in order to analyze the relevance of Zheng He historiography for the framing of national and global history in China, as well as for the country’s cultural diplomacy.

Xiaobai Hu, “Exploring the Foreign Land: The Founder of Ming China and His Tibet Experiments”

Between the two founders of Ming China, Zhu Yuanzhang and Zhu Di, scholarly attention has been quite imbalanced when it comes to their relationships with Tibet.
While Zhu Di showed great enthusiasm toward Tibet and frequently invited Tibetan hierarchs to his court, Zhu Yuanzhang’s attitude for this westerly foreign land remained understudied. This paper examines Zhu Yuanzhang’s Tibet policies in the context of Yuan-Ming transition. Being a spiritual realm during the Yuan era where Mongol Khans’ theocratic legitimacy came from, Tibet was hard to position in the Ming founder’s imagined world. Therefore, Zhu Yuanzhang constantly improvised his Tibet policies in the wake of changing geopolitical situations and for different audiences and pragmatic reasons. The first section scrutinizes Zhu Yuanzhang’s early diplomatic contacts with Tibet and challenges the tributary interpretation that dominated the scholarship of Ming-Tibet relationship. The second section examines how Zhu Yuanzhang roped Tibet with the Mongol issue from 1375 to 1380 and resorted to military and coercion policies with an aggressive attitude; The third section studies the shift of Zhu Yuanzhang’s reliance from Tibetan secular rulers to spiritual leaders. By the end of the 14th century, Hezhou–Taozhou region was chosen to be the new Tibetan Buddhist centre in contract to the previous one at Lintao during the Mongol era. It is the back-and-forth in Zhu Yuanzhang’s Tibet policies that constituted his preliminary empire-building agenda and laid the foundation for Ming-Tibet interaction in the following centuries.

Leiyun Ni, “Provision as a Negotiation Site: Sino-Anglo Encounters in Canton”

This paper aims examines the structure of food supply system of the English East India Company in Canton and its role in the power dynamics between China and Britain during the 18th and 19th centuries. Previous studies on provision for EIC focused on its features as a trade and its impact on the entire Canton system. Rather than merely regarding the food supply as a business, this paper argues that it was the provision that linked different groups of people involved in this trade. Provision kept them alive, not just physically, but also politically, socially and culturally. Provisions were essential not only because they nourished human bodies, but also because of their cultural, social and political meanings and functions that channeled this trading system. Communications, negotiations and conflicts were permeable in every process of provision system. People involved in this trade had to tackle with linguistic, geographical and cultural barriers to ensure food and drink were provided sufficiently and satisfactorily. It involved interpersonal relationships but also international and global networks. By examining the system of provision, it will help us understand the complexity of the mechanism of this global trade. I will use travel writings of individual British merchants, officers and sailors, official records of EIC in British library and National Archives and some American company’s accounts. Dictionaries in both English and Chinese published by Westerners and Chinese will also be used as my primary sources.

Tuesday
2:00 pm – 3:45 pm
Room 2

• Organised by Fei Huang
• Shuk Wah Poon, Chair
• Fei Huang, “Hot Springs, Trees and Nature at Huaqing Spa Resorts in Modern Xi’an”
• Ke Ren, “Cultural Preservation and Ethnographic Observation in Wartime China: The ‘Archaeological Travelogues’ of Wang Ziyun and He Zhenghuang”
• Pan Wei, “Mobilising Farm Households and Traditional Hydraulic System during Late Imperial and Modern Northwest China”
• Shuk Wah Poon, Discussant

As one of the most important cities in China, Xi’an served as the capital of thirteen dynasties throughout early and medieval Chinese history. After the imperial political and economic centre moved to eastern China in the tenth century, it was downgraded to a local city in the hinterland. In the late nineteenth and early-twentieth-century, both Xi’an and Northwest China were reintroduced into the public discussion as a locus from which to preserve the roots of Chinese culture and provide a last resort. Only a few works focus on later urban and agricultural developments in the modern Xi’an and the Northwest Region. This panel seeks to explore how different social actors involved in the development of modern urban reconstruction, local farming landscape and cultural preservation. It begins with Wei Pan’s investigation of the “mobilising farm household” and water management in the local society in order to reexamine the processes of modernisation in the exploitation of water resources. Fei Huang (Panel Organizer) then investigates the maintenance and reconstruction of hot springs resorts in early twentieth-century Xi’an to understand the management of cultural landscapes associated with modern developmentalism. Ke Ren studies the “archaeological travelogues” by Chinese intellectuals in their cultural preservation and ethnographic observation of Xi’an and Northwest China during the War of Resistance. Poon Shuk Wah serves Panel Chair and discussant. Through three papers, this panel allows us to rethink the Chinese hinterland city and county beyond the postcolonial or semi-colonial analytical mode, often applied to studies of Shanghai and other coastal or port cities and counties in modern China.

Fei Huang, “Hot Springs, Trees and Nature at Huaqing Spa Resorts in Modern Xi’an”

This paper focuses on the most well-known hot spring resorts in China, Huaqing Palace, and its surrounding landscape. It will first illustrate the process of its transformation from an imperial palace into a local prefecture garden in the late nineteenth century. In the first of early twentieth century, Huaqing Palace, Mount Li, and the surrounding landscape was recognized and reconstructed as a landscape maintenance district during the urban planning of the “Western Capital”. A national monumental pavilion of the “suffering of difficulties” of Chiang Kai-shek, the national leader of Republic China, was constructed on Mount Li along with the forest park to attract more tourists for history and nature tours alongside the public bathing activities. While a travel agency managed the bathing business, the forest park was under the charge of the local forest bureau for the scientific afforestation and modern forest protection. The process of establishing the forest park went along with the redefining of property rights of the lands and natural resources within this landscape maintenance district. Local inhabitants and businessmen, temple residents, mountain bandits, and tourists were all involved in this process. Huaqing Palace and the Mount Li areas became a contested space for various social actors to compete in the early twentieth century. This project will reveal how diverse perceptions and activities connected to the hot spring resorts, forest park and historical relics have been developed in both conflict and interaction with various social communities during the early twentieth century.

Ke Ren, “Cultural Preservation and Ethnographic Observation in Wartime China: The “Archaeological Travelogues” of Wang Ziyun and He Zhenghuang”

In 1940, as China’s War of Resistance against Japan settled into a stalemate, the Chinese Ministry of Education authorized a Northwest Art and Artifacts Research Team to survey artefacts and monuments in northwestern China. Headed by the sculptor Wang Ziyun (1897–1990), the group of artists engaged in a five-year intensive study of sculptures, steles, and cave paintings in the provinces of Shaanxi, Gansu, and Qinghai, including the Dunhuang caves. Using techniques such as photography, rubbings, and sketching, the group catalogued thousands of historical artworks and artefacts, hosted exhibitions, and laid the foundations for important archaeological research and historical museums. Operating in a time of national crisis, this Nationalist government-sponsored project served the dual purpose of collecting and preserving cultural artefacts while making a historical claim for Chinese civilization in the region. This research project thus mirrored the efforts by contemporary scholars to write key northwestern cities such as Xi’an into China’s modern national history. At the same time, the travel writings of Wang Ziyun and his wife and colleague He Zhenghuang (1914–1994) also included rich observations of an ethnically diverse local social life in and around Xi’an. Reading Wand and He’s diaries and published travel essays within the wartime context, this paper argues that their “archaeological travelogues” (kaogu youji) constituted both a nationalistic project of cultural preservation as well as an ethnographic portrait of northwest China. The result is a compelling record of coastal Chinese intellectuals trying to come to terms with an imagined shared past as well as a dynamic and diverse nation in the present.

Pan Wei, “Mobilising Farm Households and Traditional Hydraulic System during Late Imperial and Modern Northwest China”

Water management in late imperial Chinese local society was closely connected with the distribution of local water resources and land rehabilitation. Traditional local society in the Northwest China developed its own water policy to effectively ensure an equal distribution of resources. In the transformation of  water and irrigation management from the late imperial to modern period, increasing conflicts on the right of water usage appeared between different local social groups. Among these various social groups, the “mobilising farm household” (yiqiuhu) and its role in this transition period deserve our further attention. The term “mobilising farm household” refers to a certain farming group which constantly moved from one location to another location to continue their farming activities. Their highly mobile status, however, frequently challenged the existing local water distributing system. This paper focuses on the everyday life of the “mobilising farm household” in Minqin County in Northwest China during the agriculture landscape transformation from the mid-eighteenth century to the mid-twentieth century. It aims to demonstrate that the conflicts between mobilising farm households with other local communities, as well as the local government, strongly echoes the processes of modernization in the exploitation of water resources.

Histories of Human and Other Waste in Pre-Modern China
Tuesday
4:00 pm – 5:45 pm
Room B

• Organised by Roel Sterckx
• Roel Sterckx, “Fertilising Fields and Hearts: Human and Animal Waste in Warring States, Qin, and Han Texts”
• Armin Selbitschka, “Human Waste in Early China: An Archaeological Perspective”
• Natalie Koehle, “An Epistemic Shift in Diagnostic Practice? Examination of Excrements in Yuan Chinese Medicine”
• Jörg Henning Hüsemann, “’Treasure Manure Like Gold’—Nightsoil in Ming–Qing Agriculture”

In China, “every substance convertible to manure is diligently husbanded”, wrote Sir John Francis Davis in The Chinese: A General Description of the Empire of China and its Inhabitants (London: 1840). Reference to human and animal waste in China goes back as far as the Shang oracle bone inscriptions. While some historians have discussed the treatment of nightsoil and human waste in the late imperial and modern age, the physical and social history of human and animal excrement and the archaeology of sanitation in pre-modern China have received scant attention. This panel proposes to examine how people in pre-modern China conceived of excretion and waste. We will discuss ‘what gets left behind’ in material and textual sources and explore the dynamics of what appeared as ‘unwanted’ or ‘wanted’. We will do so from various angles including material and social history, moral and religious narrative, and agricultural and medical discourse. Each paper zooms in on a different time period and/or set of sources ranging from early China, through to the Yuan, Ming, and Qing.

Roel Sterckx, “Fertilising Fields and Hearts: Human and Animal Waste in Warring States, Qin, and Han Texts”

Early Chinese texts contain several stories and metaphors identifying the latrine and excrement with the lower domains of human morality. According to the opening passage of his biography in Sima Qian’s 司馬遷 Historical Records (Shiji 史記), Li Si 李斯, the later chancellor to China’s First Emperor, was so disgusted at the sight of rats eating the filth in the privy of the clerk’s quarters where he served during his youth, that it inspired him to become an adept administrator and chief planner. The privy was a liminal space where contact with waste could soil a person’s social reputation. Defecation or the handling of faeces could make the body vulnerable to demonic influences. On the other hand, excrement also figured as a substance associated with growth and fertility. This paper examines attitudes towards human and animal excrement in texts of the Warring States, Qin and Han periods against their documented use in religious practices, agriculture and medicine.

Armin Selbitschka, “Human Waste in Early China: An Archaeological Perspective“

By and large, scholars of early China do not seem to be too keen on speaking about faeces. Apart from brief discussions of the medicinal uses of (human) excrements in Traditional Chinese Medicine and fleeting references to their apotropaic functions, scholarship remains largely silent on the issue. At first glance, that is all too understandable. On the one hand, faeces may appear repulsive to most observers. On the other, they literally are (human) waste, and as such either flushed down the sewer or buried in the ground.
However, since archaeology is the science of digging up remnants of human life, it might offer a more nuanced perspective. Thus, by analysing excavated latrines and model privies yielded by early imperial Chinese tombs (ca. 2nd c. BCE–3rd c. CE) in concert with some received literature, I will argue that we would do excrements a great disservice by assuming that they lost all meaning once they were discharged. Quite the contrary was true. The archaeological record shows that faeces, much like today, fulfilled a vital role in the production of food in early China.

Natalie Koehle, “An Epistemic Shift in Diagnostic Practice? Examination of Excrements in Yuan Chinese Medicine“

If you wanted to know what’s going on inside your body, where would you look?
Bodily discharges seem like an obvious place. Hippocrates and Galen routinely scrutinised sputa, stool and urine, and by and large, these practices still appear to make sense to us today. But the intuition to search for signs of physiological processes in bodily outflows is not universal. Classical Chinese doctors paid scant attention to the appearance of excrement. Its sensory qualities, as perceived by sight, smell, and structure of bodily discharges outside of the body, were first described in 1327, in a treatise on phlegm. Many concepts and practices in this treatise, composed by the Daoist recluse Wang Gui 王珪 (1264–1354), were entirely unprecedented in Chinese medicine. At the same time, they resembled core concepts and practices of Greco-Islamic medicine.
This paper will analyse Wang Gui’s conceptual and diagnostic innovations. It will situate them in the context of contemporary Chinese medical debates and compare them to similar practices in Galenic medicine. I suggest that we should understand Wang Gui’s innovations as a response to his encounter with the Galenic medical tradition, as practised by Islamic doctors in Yuan China (1271–1368). I will draw attention to the different meanings of Wang Gui’s vs Galenic examinations of bodily discharges. Which concepts and practices were transmitted in this particular instance of a practical (and likely non-textual) knowledge transmission? And why?

Jörg Henning Hüsemann, “’Treasure Manure Like Gold’—Nightsoil in Ming–Qing Agriculture“

“Treasure manure like gold” was something which according to Yuan 元 (1279–1368) scholar Wang Zhen 王禎 (fl. 1271–1333) “only those who devote themselves to the foundation 本 (i.e. agriculture) know about”. Like Wang Zhen, many authors of agricultural writings (nongshu 農書) regarded the application of fertilisers as an important part of the farmers’ work. Among the dozens of different materials Chinese peasants used for fertilising their fields, human excreta were of particular importance. In pre-Song 宋 (960–1279) sources, reports about fertilisers are relatively scarce and it was only in later writings that authors dealt in greater detail with the materials and techniques used to improve soil quality. As part of this development, they also recorded explanations to elucidate what is a fertiliser, how it works and why it is important to fertilise fields. Human excrements were often valued as the most effective fertiliser and farmers travelled distances to acquire nightsoil from larger settlements and cities. Over time, trading nightsoil developed into a well-organized and profitable business. Westerners travelling the Chinese empire also noticed the use of human waste in agriculture and frequently discussed this topic in their writings. Using a variety of sources, I will discuss how Chinese and Westerners wrote about nightsoil and assessed its value for Chinese agriculture, thereby shedding more light on how Chinese farmers turned waste into money.

In Ancient Chinese Mathematical and Cosmographical Treatises
Tuesday
2:00 pm – 3:45 pm
Room B

• Alexei Volkov, “Textual Structures in Ancient Chinese Mathematical Treatises: On textual Parallelisms, Analogical Reasoning and Didactical Variables”
• Karine Chemla, “The Nine Chapters on Mathematical Procedures 九章算術: A Formal Structure with a Cosmological Meaning?”

The main goal of this panel is to discuss non-linear textual structures in Chinese sources relevant to the history of science, in particular, in mathematical and cosmographical texts. The contributions of Volkov and Chemla deal with the structures of early Chinese mathematical texts, while the paper of Dorofeeva-Lichtmann is focused on the early Chinese cosmographic descriptions. This approach to these two categories of texts, even though representing two markedly different fields of proto-scientific expertise, reveal a number of common features worth a thorough investigation. Chemla suggests that the reading of the Han dynasty mathematical treatise Jiu zhang suan shu 九章算術 by its commentators Liu Hui 劉徽 (fl. AD 263) aimed at the identification of structural elements of the treatise which, according to him, may have been lost in the Han 漢 dynasty edition of the treatise. In turn, in his paper, Volkov discusses an earlier study of the Jiu zhang suan shu by the Russian sinologist V.S. Spirin (1929–2002) who identified a non-linear structure in chapter nine of the treatise. Volkov evaluates Spririn’s reconstruction and identifies other non-linear structures in this text. In her paper, Dorofeeva-Lichtmann suggests that there existed a direct link between the early Chinese cardinally-oriented textual structures and textual interpolations found in the extant traditional Chinese maps of Imperial China from the 12th century onwards.

Alexei Volkov, “Textual Structures in Ancient Chinese Mathematical Treatises: On textual Parallelisms, Analogical Reasoning and Didactical Variables”

The paper will begin with a critical evaluation of V.S. Spirin’s (1929–2002) reconstruction of a “nine-term structure” that he discovered in the ninth chapter of the ancient Chinese mathematical treatise Jiu zhang suan shu 九章算術. Spirin’s analysis was published in 1976 in his monograph The Structure of Ancient Chinese Texts (published in Russian) and remained practically unknown to historians of Chinese mathematics. I will critically evaluate Spirin’s analysis and discuss the structures that can be identified in this and other Chinese mathematical treatises. In particular, I will focus on the two following types of structures. The first type is represented by a series of mathematical problems related to the computation of the areas and volumes described in chapters one, four and five of the Jiu zhang suan shu. In this part, I will discuss the interrelationships between the methods that may have been generated by analogical transfer from two-dimensional to three-dimensional case and will explain how the analogical reasoning of this kind may have been interrelated with the structure of this mathematical texts. The second type of structures is related to the didactical dimension of the mathematical treatises; I will show how certain parameters arguably used as didactical variables determined the structure of sequences of problems found in the Jiu zhang suan shu and in other pre-modern Chinese mathematical treatises as well as in later Vietnamese mathematical texts.

Karine Chemla, “The Nine Chapters on Mathematical Procedures 九章算術: A Formal Structure with a Cosmological Meaning?”

The Nine Chapters was completed, in my view, in the first century. Several commentaries on it were handed down, two of them featuring in all the ancient editions. They are the commentary completed by Liu Hui in 263, and the sub-commentary presented by Li Chunfeng to the throne in 656. The commentators made declarations about mathematics or about The Nine Chapters. I have argued that we can interpret these declarations as stating that the two opposed but complementary operations of multiplication and division played a fundamental role in The Nine Chapters or, more generally, in mathematics, which The Nine Chapters displayed since, for the exegetes, it embodied the whole of mathematics. As its title makes clear, the work is composed of nine chapters. My talk draws on this former result to suggest that the earliest known commentaries read a structure in The Nine Chapters that opposed two parts. The first part displayed mathematical patterns of combination of multiplication and division, while the second featured the same patterns repeated. This reading sheds unexpected light on the addition to the canon that Liu Hui composed in the context of his commentary. Indeed, for him, The Nine Chapters as transmitted failed to restore the original canon destroyed by the Qin books burning. His addition, which purports to rely on ancient documents, can be read as completing the canon with respect to the structure described.